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1 Tanaka, Hiro Lee Lectures on Factorization Homology, ???-Categories, and Topological Field Theories I09620 2020 eBook  
2 Ku??, Marek Category Theory in Physics, Mathematics, and Philosophy I08612 2019 eBook  
3 Coecke, Bob Current Research in Operational Quantum Logic I11348 2000 eBook  
4 Husem??ller, Dale Basic Bundle Theory and K-Cohomology Invariants I08348 2008 eBook  
5 Unterberger, J??r??mie The Schr??dinger-Virasoro Algebra I08215 2012 eBook  
6 Kapustin, Anton Homological Mirror Symmetry I07440 2009 eBook  
7 Coecke, Bob New Structures for Physics I07027 2011 eBook  
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TitleLectures on Factorization Homology, ???-Categories, and Topological Field Theories
Author(s)Tanaka, Hiro Lee
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2020.
DescriptionXII, 84 p. 13 illus., 2 illus. in color : online resource
Abstract NoteThis book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples. Along the way, the reader is also introduced to modern ideas in homotopy theory and category theory, particularly as it relates to the use of infinity-categories. As with the original lectures, the text is meant to be a leisurely read suitable for advanced graduate students and interested researchers in topology and adjacent fields
ISBN,Price9783030611637
Keyword(s)1. ALGEBRAIC TOPOLOGY 2. Category theory (Mathematics) 3. Category Theory, Homological Algebra 4. EBOOK 5. EBOOK - SPRINGER 6. Homological algebra 7. MATHEMATICAL PHYSICS 8. Theoretical, Mathematical and Computational Physics
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TitleCategory Theory in Physics, Mathematics, and Philosophy
Author(s)Ku??, Marek;Skowron, Bart??omiej
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2019.
DescriptionXII, 134 p. 3 illus., 1 illus. in color : online resource
Abstract NoteThe contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes. The book approaches formal ontology in the original sense put forward by the philosopher Edmund Husserl, namely as a science that deals with entities that can be exemplified in all spheres and domains of reality. It is a dynamic, processual, and non-substantial ontology in which all entities can be treated as transformations, and in which objects are merely the sources and aims of these transformations. Thus, in a rather surprising way, when employed as a formal ontology, category theory can unite seemingly disparate disciplines in contemporary science and the humanities, such as physics, mathematics and philosophy, but also computer and complex systems science
ISBN,Price9783030308964
Keyword(s)1. Category theory (Mathematics) 2. Category Theory, Homological Algebra 3. EBOOK 4. EBOOK - SPRINGER 5. Homological algebra 6. Mathematical Methods in Physics 7. MATHEMATICAL PHYSICS 8. Mathematics???Philosophy 9. PHILOSOPHY OF MATHEMATICS 10. PHYSICS 11. QUANTUM PHYSICS
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TitleCurrent Research in Operational Quantum Logic : Algebras, Categories, Languages
Author(s)Coecke, Bob;Moore, David;Wilce, Alexander
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2000.
DescriptionVII, 325 p : online resource
Abstract NoteThe present volume has its origins in a pair of informal workshops held at the Free University of Brussels, in June of 1998 and May of 1999, named "Current Research 1 in Operational Quantum Logic". These brought together mathematicians and physicists working in operational quantum logic and related areas, as well as a number of interested philosophers of science, for a rare opportunity to discuss recent developments in this field. After some discussion, it was decided that, rather than producing a volume of conference proceedings, we would try to organize the conferees to produce a set of comprehensive survey papers, which would not only report on recent developments in quantum logic, but also provide a tutorial overview of the subject suitable for an interested non-specialist audience. The resulting volume provides an overview of the concepts and methods used in current research in quantum logic, viewed both as a branch of mathemati?? cal physics and as an area of pure mathematics. The first half of the book is concerned with the algebraic side of the subject, and in particular the theory of orthomodular lattices and posets, effect algebras, etc. In the second half of the book, special attention is given to categorical methods and to connections with theoretical computer science. At the 1999 workshop, we were fortunate to hear three excellent lectures by David J. Foulis, represented here by two contributions. Dave's work, spanning 40 years, has helped to define, and continues to reshape, the field of quantum logic
ISBN,Price9789401712019
Keyword(s)1. ALGEBRA 2. Applications of Mathematics 3. APPLIED MATHEMATICS 4. Category theory (Mathematics) 5. Category Theory, Homological Algebra 6. EBOOK 7. EBOOK - SPRINGER 8. ENGINEERING MATHEMATICS 9. GROUP THEORY 10. Group Theory and Generalizations 11. Homological algebra 12. Order, Lattices, Ordered Algebraic Structures 13. Ordered algebraic structures 14. QUANTUM PHYSICS
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TitleBasic Bundle Theory and K-Cohomology Invariants
Author(s)Husem??ller, Dale;Joachim, Michael;Jurco, Branislav;Schottenloher, Martin
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2008.
DescriptionXV, 340 p : online resource
Abstract NoteBased on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory with the aim to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object. One renewed motivation for studying this subject, which has developed for almost 50 years in many directions, comes from quantum field theory, especially string theory, where topological invariants play an important role
ISBN,Price9783540749561
Keyword(s)1. Category theory (Mathematics) 2. Category Theory, Homological Algebra 3. EBOOK 4. EBOOK - SPRINGER 5. Homological algebra 6. Mathematical Methods in Physics 7. PHYSICS
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TitleThe Schr??dinger-Virasoro Algebra : Mathematical structure and dynamical Schr??dinger symmetries
Author(s)Unterberger, J??r??mie;Roger, Claude
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2012.
DescriptionXLII, 302 p : online resource
Abstract NoteThis monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure???the Schr??dinger-Virasoro algebra. Just as Poincar?? invariance or conformal (Virasoro) invariance play a key role in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence. ?? The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and the spectral theory of Schr??dinger operators.
ISBN,Price9783642227172
Keyword(s)1. Category theory (Mathematics) 2. Category Theory, Homological Algebra 3. COMPLEX SYSTEMS 4. DYNAMICAL SYSTEMS 5. EBOOK 6. EBOOK - SPRINGER 7. Homological algebra 8. LIE GROUPS 9. Mathematical Methods in Physics 10. MATHEMATICAL PHYSICS 11. PHYSICS 12. STATISTICAL PHYSICS 13. Statistical Physics and Dynamical Systems 14. TOPOLOGICAL GROUPS 15. Topological Groups, Lie Groups
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TitleHomological Mirror Symmetry : New Developments and Perspectives
Author(s)Kapustin, Anton;Kreuzer, Maximilian;Schlesinger, Karl-Georg
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2009.
DescriptionXI, 272 p : online resource
Abstract NoteHomological Mirror Symmetry, the study of dualities of certain quantum field theories in a mathematically rigorous form, has developed into a flourishing subject on its own over the past years. The present volume bridges a gap in the literature by providing a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives. With contributions by K. Fukaya, M. Herbst, K. Hori, M. Huang, A. Kapustin, L. Katzarkov, A. Klemm, M. Kontsevich, D. Page, S. Quackenbush, E. Sharpe, P. Seidel, I. Smith and Y. Soibelman, this volume will be a reference on the topic for everyone starting to work or actively working on mathematical aspects of quantum field theory
ISBN,Price9783540680307
Keyword(s)1. Category theory (Mathematics) 2. Category Theory, Homological Algebra 3. EBOOK 4. EBOOK - SPRINGER 5. Homological algebra 6. Mathematical Methods in Physics 7. PHYSICS 8. Quantum Field Theories, String Theory 9. QUANTUM FIELD THEORY 10. STRING THEORY
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TitleNew Structures for Physics
Author(s)Coecke, Bob
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2011.
DescriptionXVIII, 1031 p : online resource
Abstract NoteThis volume provides a series of tutorials on mathematical structures which recently have gained prominence in physics, ranging from quantum foundations, via quantum information, to quantum gravity. These include the theory of monoidal categories and corresponding graphical calculi, Girard???s linear logic, Scott domains, lambda calculus and corresponding logics for typing, topos theory, and more general process structures. Most of these structures are very prominent in computer science; the chapters here are tailored towards an audience of physicists
ISBN,Price9783642128219
Keyword(s)1. Category theory (Mathematics) 2. Category Theory, Homological Algebra 3. COMPUTERS 4. EBOOK 5. EBOOK - SPRINGER 6. Homological algebra 7. Mathematical Methods in Physics 8. PHYSICS 9. Theory of Computation
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